INTERNAL REAL RATES OF RETURN UNDER THE OASDI PROGRAM
FOR HYPOTHETICAL WORKERS

by Orlo R. Nichols, Michael D. Clingman, and Milton P. Glanz

Introduction

This note presents analysis of internal real rates of
return for hypothetical workers with various earnings patterns and levels
under the Old-Age, Survivors and Disability Insurance (OASDI) program. The
internal real rate of return (hereinafter referred to as the internal rate
of return) is the real interest rate (effective real annual yield) for
which the present value of expected payroll taxes is equal to the present
value of expected benefits. Therefore, internal rates of return represent
an attempt to answer the question: If the contributions of a group of
workers with selected characteristics were invested to fund the future
benefits of the workers and their dependents, at what real annual yield
would the contributions need to be invested
1?
Because contributions are not expected to be
sufficient to fully finance scheduled benefits after 2037, analysis is
included for the OASDI program both as in present law, and with assumed
future increases in contribution rates that would fully finance the
benefits of present law.

Because the Social Security program has operated on a
largely pay-as-you-go (PAYGO) basis, the level of contributions of each
generation of workers is not directly related to the benefits they will
receive. Under a PAYGO plan, benefits are not based on the accumulation of
individual contributions, as in a defined contribution plan, nor are
annual contributions determined based on scheduled future benefits of
current workers and beneficiaries, as in an advance-funded defined benefit
plan. Rather, the combined amount of contributions from workers needed to
fund the system at any time has been largely determined by the combined
amount of benefits paid at that time. The internal rates of return depend
on the contribution tax rates and Social Security benefit levels set by
Congress. They do not in any significant way reflect the rate of interest
on assets invested in the OASI and DI Trust Funds.

Internal rate of return does not reflect the full value
of insurance in reducing the risk for extreme outcomes, like death or
disability at very young ages or survival to very old ages. In addition,
calculations of the internal rate of return from Social Security benefits
are not fully adequate for making comparisons with private-sector plans,
since many features of Social Security benefits are not typically
available in private-sector plans. Examples include guaranteed
cost-of-living adjustments based on the Consumer Price Index, and benefits
for life in the event of disability. However internal rates of return are
of value for exploring the relative value of benefits provided across
generations and types of workers.

Hypothetical workers are presented in this note with two
types of earnings patterns. These are designated as
steady and scaled . A worker with a steady pattern has earnings that are a constant
percentage of the average wage2 for each year of work. A worker with a
scaled earnings pattern has earnings that vary
with age as a percentage of the average wage. Steady workers are assumed
to enter covered employment at age 22 and remain employed until
disability, death, or retirement at age 65. Scaled workers are assumed to
enter the labor force at age 21, and reflect varying rates of employment
until disability, death, or retirement at age 65.

The Office of the Chief Actuary has for years been
producing internal rates of return. An example can be found in Appendix II
of Volume I of the 1994-96 Advisory Council Report on Social Security. The
office has only recently developed an approach for representing non-steady
hypothetical workers, referred to in this note as scaled workers.
Alternative approaches to considering non-steady earnings histories have
been addressed by other authors, and it is recognized that a broader set
of earnings patterns might be desirable to more fully explore the
distributions of benefits payable and internal rates of return under the
OASDI program. However, for the sake of practicality, the number of cases
considered in this note is limited.

Internal rates of return are presented in tables 3, 4, 5,
and 6 for hypothetical workers who differ by year of birth, earnings
level, family grouping, and earnings pattern (steady and scaled).

Methodology and Assumptions

Computation of internal rates of return requires a
complete simulation of the experience of each hypothetical group of
workers for all years after first entering the labor force (assumed at age
21 or 22 for this note). The possibility of dying or becoming disabled in
each year after entering the labor force must be taken into account.
Actual experience is used for historical years. Projections of future
experience are based on the intermediate assumptions of the 2001 Trustees
Report. While it is recognized that mortality and disability both tend to
be higher for lower paid workers, this fact is not reflected in the cases
presented in this note. Further analysis will be necessary to properly
address this issue. We have chosen hypothetical cases with 11 different
years of birth from 1920 through 2004 to demonstrate the variation in
internal rates of return across generations. Our analysis includes the
payment of all OASDI benefits for death, disability, and retirement,
reflecting historical and projected probabilities of death, disability,
and recovery from disability. Retirement is assumed to be at age 65 for
non-disabled workers.

As mentioned above, two types of hypothetical earnings
patterns are presented, steady and scaled. The steady
earnings pattern assumes that the worker is a steady full-time employee
with no interruptions in employment. The steady
worker begins working in covered employment at age 22 and the worker's
earnings increase each year at the same rate as the average wage. The
steady worker is assumed to stay employed,
except for periods of disability, until death, or until retirement at age 65.
For the steady earnings pattern, the following
four levels of earnings are presented in tables 3, 4, 5, and 6.

Maximum:
Annual earnings are equal to the OASDI Contribution and Benefit Base
4.

The OASDI benefit levels associated with these four
earnings levels "best represent"5 different proportions of the male, as
compared with the female, worker populations. The table below summarizes the
representation of actual male and female retirees in 1999 by these four
cases. Additional discussion of the distributions illustrated in this
table is included in the section "Discussion of Worker Earnings and
Benefit Levels".

1 Primary Insurance Amount. The PIA is the full
(that is, unreduced) monthly benefit level, which is payable to disabled
workers and to retired workers who become entitled at normal retirement
age.

2 May not add to 100 percent due to
rounding.

It should be noted that the percentages indicated above
reflect the status of workers retiring in 1999, and that these percentages
would be different for workers retiring in earlier or later years. For
example, the increasing employment rates for women over the last several
decades is expected to result in relatively greater increases in
career-average earnings for women than for men in the future. Therefore,
the difference in the distributions of male and female retired workers by
benefit levels is expected to diminish in the future.

In actuality, the year-to-year earnings of most workers
do not follow these steady earnings patterns. Career earnings often start
out at a relatively low level in the early years of employment, increase
rapidly and peak in mid career, and then level off or even decline
somewhat in later years. In addition, workers do not necessarily work in
every year after entering the labor force and prior to disability, death,
or retirement. To reflect these patterns, alternative cases, which are
designated as scaled , are presented. These
scaled cases were developed using available sample
earnings data for workers who are fully insured under the OASDI program.
They take into account changes in earnings levels by age as well as
periods of unemployment or withdrawal from the labor force. However,
"maximum" workers are assumed to have steady maximum earnings
starting at age 22 and thus equal to the steady worker cases.

To maintain comparability with the hypothetical
steady worker cases that have been used in the
past, earnings for the scaled workers were
adjusted to produce equivalent Social Security retirement benefit levels.
For each earnings level (low, medium, or high), year of birth, and family
grouping, the earnings of the worker with the
scaled earnings pattern is multiplied by that constant factor which
produces the same AIME 6
(and, consequently, the same Social Security retirement benefit) as the
corresponding worker with steady earnings
7.

The resulting internal rate of return for the scaled
worker turns out to be somewhat higher than that for the corresponding
steady worker, even though retirement benefits are the same. As shown in
the Appendix, more earnings are paid later in life for the scaled worker,
making the average time between when taxes are paid and when benefits are
received less than for the steady worker. This shorter period of time
between when taxes are paid and benefits are received for scaled workers
results in a higher internal rate of return. However, for disability
benefits no uniform relationship between internal rates of return for
steady and scaled earnings records is evident.

For this note, internal rates of return were determined
for two specifications of the OASDI program, Present
Law and PL PAYGO . The
Present Law specification is based on the taxes and
benefits specified in present law, assuming no future legislative changes.
However, the program income and assets under present law are projected to
be inadequate to fully pay all benefits through the 75-year projection
period. Therefore we also present an analysis based on a set of modified
payroll-tax rates, called PL PAYGO . Under the
PL PAYGO specification, payroll-tax rates are
assumed to be increased as needed so that present-law benefits would
always be payable and that the amount of assets in the combined OASI and
DI Trust Funds would always equal at least one year's outgo. The
PL PAYGO payroll-tax rates begin to increase over
the Present Law rates in 2025 and reach 17.2
percent by 2060. The schedule of tax rates for
Present Law and for PL PAYGO , under the
intermediate assumptions of the 2001 Trustees Report, are shown below.

It is expected that further increases in
PL PAYGO tax rates would be needed after 2075 due
to continuing increases in life expectancy.

Internal rates of return for the first six year-of-birth
cohorts studied are the same for both Present
Law and PL PAYGO for every family
grouping, every earnings level and for both steady and scaled earnings;
since each of these year-of-birth cohorts reaches age 65 prior to 2025
(when the PL PAYGO first departs from the Present Law tax schedule).

The hypothetical workers presented in this note are
grouped by sex and family grouping into four categories: single males,
single females, one-earner couples where only the husband is employed, and
two-earner couples. The single-earner examples are presented for all four
earnings levels listed above. The two-earner couples are presented at five
earnings combinations as follows:

Each worker is assumed to enter the labor market on his
or her 22nd birthday if earnings are
steady, 21st
if they are scaled. Because labor force participation rates are
relatively low at younger ages, steady workers are assumed to start at a
higher age than the scaled workers, who reflect varying probabilities of
employment. The wife and husband of each couple are assumed to have the
same date of birth. Each marriage is assumed to occur on the joint 22nd birthday of the wife and husband and to
continue for life. Two children are assumed, one born on the joint 25th birthday of the wife and husband, and one
born on the joint 27th birthday of the
wife and husband. All types of retirement, disability, and survivor
benefits are considered, except for benefits to student children, benefits
to disabled-adult children, and benefits to parents based on caring for a
disabled-adult child. Omission of these benefits results in a negligible
understatement of the real internal rate of return.

The mortality rates and disability incidence and
termination rates used in these computations are taken from historical
data, and from the intermediate projections of the 2001 Trustees Report by
age, sex, and date of birth. No mortality is assumed for children through
age 18 in this analysis. Assuming that marriages are lifelong means that
the effects of divorce and of remarriage after death and divorce are not
explicitly reflected. However, because each individual may receive a total
benefit equal only to the highest of any spouse, widow(er), or worker
benefit that may be available, this omission is of minor consequence.
Benefit increases and earnings levels are based on actual data for the
past and the 2001 Trustees Report assumptions for the future.

Analysis of Results

The following tables present the calculated internal
rates of return. The tables are intended to facilitate comparison of rates
of return across different family groups, different years of birth,
different career-average levels of earnings, and whether the earnings
pattern is steady or
scaled.

Table 3.--Internal Real Rates of Return for Various Earnings Level Workers Under
Present Law OASDI Program

Tables 3 through 6 present results for single males,
single females, one-earner couples, and two-earner couples, for both the
steady and scaled
earnings patterns and for both the Present Law
and PL PAYGO OASDI program specifications. For
each sex, family grouping, and year-of-birth cohort the internal rates of
return decrease as earnings increase. This is because the benefit formula
is weighted toward beneficiaries with lower earnings. Females have lower
mortality than males, resulting in longer life after retirement and
therefore higher internal rates of return, even when earnings levels are
the same. This effect is only partially offset by lower rates of
disability for women. The one-earner couples have the highest rates of
return because of the auxiliary spouse, child, and widow(er) benefits
payable based on one earnings record.

For two-earner couples the internal rates of return
generally fall between the corresponding rates for single male and single
female workers, and are much closer to the rates for females. Where both
spouses have the same earnings (tables 3 and 4), the internal rate of
return for the two-earner couple is closer to the higher (female) single
internal rate of return because of the inclusion of child benefits not
reflected for single cases. Where spouses have different earnings levels
(tables 5 and 6), the two-earner internal rate of return is closer to the
single female internal rate of return. This is for the reason stated
above, plus the fact that a significant additional surviving spouse
benefit may be payable to the lower earner (female in these examples). For
the cases chosen for this note, the wife's retired worker benefit is more
than half of that of her husband's, so no spouse's benefit is payable.

It should be noted that this note does not include cases
where a single individual has children, an increasingly common occurrence.
Future analyses may address these cases. For now, it can be assumed that
the internal rate of return for such cases would fall between those for
the single worker and one-earner couple.

Comparing two hypothetical cases that only differ by
whether career earnings are steady or
scaled, the internal rates of return are generally
higher for the scaled worker than for the steady worker. The career
earnings of the scaled worker are designed to
produce the same average indexed monthly earnings at age 65 as those of
the steady worker.
Thus, the benefit levels are the same for retirement at 65,
but differ in cases of disability and death prior to retirement.

Based on general considerations of the rising tax rates
of the OASDI Program (combined employer and employee tax went from 2
percent in 1940 to 12.4 percent starting in 1990), and the declining
relative value of benefits due to an increase in the retirement age, one
might expect that the internal rate of return would decline steadily as
the year of birth advances. Tables 3, 4, 5, and 6 show internal rates of
return for a series of birth cohorts for 68 combinations of sex, family
grouping, earnings level, and projected tax rates (
Present Law and PL PAYGO),
which permit us to test this expectation.
Every one of the 68 combinations show substantial decreases in the
internal rates of return for the first four year-of-birth cohorts (1920,
1930, 1937, and 1943), but for subsequent birth cohorts the expectation is
not always borne out. For the Present Law tax
schedule combinations (tables 3 and 5), the
internal rates of return increase continually
beginning with the 1985 birth cohort, due to improving mortality rates
combined with a fixed Normal Retirement Age (NRA) and a fixed tax rate.
For the years between--the birth cohorts 1949, 1955, 1964, and 1973--there
is no consistency from series to series. For the PL PAYGO tax schedule
combinations (tables 4 and 6), the
internal rate of return decreases continually
beginning with the 1964 birth cohort in table 4 and the 1955 cohort in
table 6. These decreases in the internal rates of
return for successive birth cohorts may reasonably be attributed to the
increasing tax rates under PL PAYGO
for years beginning 2025. For the
years between--1949 and 1955--as with the in-between years for the Present Law schedule, again there is no consistent
pattern from series to series.8

The NRA was set at age 65 in the original Social Security
Act of 1935. Increases in the NRA have already started, as of 2000, as
specified by the Social Security Amendments of 1983. The NRA is scheduled
to be age 65 for those born before 1938, to increase by two months each
year for those born from 1938 through 1943, to remain at age 66 for those
born from 1944 through 1954, and then to again increase by two months each
year until reaching age 67 for those born in 1960. The NRA is currently
scheduled to remain at age 67 for those born after 1960.

The table below presents the projected increases in
average wages, and the cost-of-living benefit increases, assumed for the
intermediate assumptions of the 2001 Trustees Report. Average wage
increases are used to determine the benefit formula adjustments so that
initially awarded benefit levels (PIAs) generally increase from
year-to-year as average wage levels increase. Benefits for those already
on the rolls are increased with the cost-of-living benefit increase.
Future increases in the average wage are assumed to be greater than future
increases in the cost of living, reflecting an assumed positive growth in
real earnings. Greater real wage increases tend to lead to higher internal
rates of return under a pay-as-you-go financed program like OASDI. The
rates of return are also affected by changes in mortality and disability
incidence and termination rates. Internal rates of return will generally
increase with improvements in mortality and worsening of disability
incidence experience under a pay-as-you-go financed program like
OASDI.

Table 7.--Average-Wage and Cost-of-Living Benefit Increases Under the
Intermediate Assumptions of the 2001 Trustees Report

(Percent)

Year

Averagewage increase

Cost-of-livingbenefit
increase

2001

4.9

2.8

2002

4.7

2.9

2003

4.3

3.0

2004

4.3

3.1

2005

4.4

3.2

2006

4.4

3.3

2007

4.2

3.3

2008

4.2

3.3

2009

4.3

3.3

2010+

4.3

3.3

Discussion of Worker Earnings and Benefit Levels

The scaled earnings pattern was developed to address the
fact that the steady earnings pattern is not realistic for computing
benefit levels under some proposals. In developing the scaled earnings
pattern, we focused on the relative level of earnings, and relative
probability of having any earnings, by age of worker. A separate issue is
the general level of earnings over a worker's entire career. To remain
consistent with past benefit illustrations, we set the overall career
earnings levels for the low, medium, and high scaled earnings patterns at
levels that are equivalent to those of the corresponding hypothetical
steady earners.

In order to properly interpret the meaning of values for
these hypothetical workers, it is useful to know where, in the
distribution of actual benefit levels, the benefits for our hypothetical
workers fall. A hypothetical steady average worker retiring at age 62 in
1999 would have a PIA of $1,025.00. Similar steady low-wage and high-wage
workers would have PIAs of $622.50 and $1,329.20, respectively. Based on a
1-percent sample of new retired worker awards in 1999
9, we find that about
28 percent of these new retirees receive benefits at or below that for a steady
low-wage worker, 30 percent receive benefits between those for steady
low-wage and steady average-wage workers, 28 percent receive benefits
between those for a steady average-wage and steady high-wage worker, and
14 percent receive benefits over the level for a steady high-wage worker.
In total, about 58 percent of retirees receive benefits less than those of
the hypothetical steady average worker and 42 percent receive higher
benefits.

The distribution of actual benefits is quite different
for newly awarded male, as compared with newly awarded female, retired
workers. The benefit for the hypothetical steady average worker is low in
the distribution of actual male retiree benefits, but is high in the
distribution of female retiree benefits. Approximately 66 percent of males
retiring in 1999 received benefits higher than that of the steady average
worker, while 87 percent of females received benefits below that level.
This is fairly consistent with an earlier note 10 that found that 60 percent of males
retiring at age 62 in 1982 had benefits over that of a corresponding steady
average worker.

Also of interest is the percentage of actual retirees
that is "best represented"5
by each type of hypothetical worker provided in
table 1. Approximately 44 percent of
1999 newly-awarded retired workers are best represented by the
hypothetical low-wage worker, 25 percent by the average-wage worker, 25
percent by the high-wage worker, and 6 percent by the maximum-wage worker.
Approximately 6 percent of workers retiring in 1999 received benefits that
were less than half the benefit of a hypothetical low-wage-steady worker.
Considering males alone, approximately 20 percent are best represented by
the low-wage earner, 28 percent by the average-wage earner, 41 percent by
the high-wage earner, and 10 percent by the maximum-wage earner. Only 2
percent of these male retirees receive benefits less than half that of a
low-wage-steady worker. For females, the corresponding values are: 72
percent are best represented by the low-wage earner, 22 percent by the
average-wage earner, 6 percent by the high-wage earner, and under 1
percent by the maximum-wage earner. Just over 10 percent of these female
retirees had benefits that were under half that of the low-wage earner.
The median PIA for males retiring in 1999 falls between the hypothetical
steady average and high workers. However, the median PIA for females is
closest to that of the hypothetical low-wage earner, and may be said to be
best represented by this earnings pattern.

Conclusions

In this note we present internal real rates of return
over time for various illustrative demographic groups and earnings levels.
However, we recognize that a variety of other approaches, methods and
assumptions can be used in this type of analysis. We believe these
hypothetical examples provide useful insight into how internal rates of
return vary over generations, and by sex, earnings level and pattern, and
family grouping.

Realistic earnings patterns are essential in determining
realistic internal rates of return for workers and for computing
accumulations of and distributions from individual accounts under a number
of proposals. Because scaled earnings patterns concentrate earnings
somewhat later in a career than do steady earner patterns, the scaled
pattern results in slightly higher internal real rates of return under the
OASDI program, and slightly lower accumulations for individual accounts

The significance of the internal rate of return must be
kept in proper perspective. A higher internal rate of return does not
necessarily mean a higher monthly benefit, even for two individuals with
the same earnings. As one example, consider a man and a woman with the
same earnings. A woman born in 1975 may expect to live 20.13 years after
the Normal Retirement Age of 67. Her male counterpart born in 1975 may
expect to live 17.16 years after age 67 11. Her expected number of years of life after
age 67 exceeds that of her male counterpart by 17 percent, and, as a result,
her internal rate of return is considerably more than her male counterpart
with the same earnings record 12. However, the monthly benefit she receives
is exactly the same as for her male counterpart. Her higher internal rate of
return derives solely from her longer expected lifetime.

Based on the provisions for benefits in the Social
Security Act that have evolved since 1935, it is clear that the goal for
the program has been to provide similarly adequate monthly benefits for
men and women, and for married and non-married workers. The goal has not
been to provide similar internal rates of return for these groups. Thus,
while this note illustrates the fact that the internal rate of return has
varied considerably and will continue to do so in the future, it is clear
that this kind of variation was both expected and intended.

Appendix

METHODOLOGY FOR DEVELOPING SCALED WORKER FACTORS

Introduction

Hypothetical earnings histories have traditionally been
used by the Office of the Chief Actuary to illustrate a range of benefit
levels, replacement rates, money's worth measures, time to recover
contributions, and internal rates of return under the Social Security
program. These illustrations have long been used to evaluate the program
under present law, but have increasingly been used to evaluate the effects
of possible alternatives. The traditional hypothetical workers that have
been used are "steady" workers. They have been assumed to work
steadily beginning at age 22, until retirement, death, or disability, and
to have a steady amount of earnings relative to the official SSA Average
Wage Index (AWI) each year. For example, the "steady average"
worker is assumed to earn the AWI for every working year. Similarly, the
"steady low" worker is assumed to earn 45 percent of the AWI for
every working year, and the "steady high" worker is assumed to
earn 160 percent of the AWI for every working year. The "steady
maximum" worker is assumed to earn the maximum taxable earnings (the
"earnings base") in every working year.

These hypothetical steady earnings histories tend to
over-represent the proportion of actual lifetime earnings received at
younger ages and under-represent the proportion received at prime working
ages for most workers. Sample data show that it is fairly typical for
workers' earnings to start out relatively low at young ages, to rise
rapidly as they initially gain experience, and then to increase more
gradually, or level off, at older ages.

Though somewhat unrepresentative, the hypothetical steady
workers have the advantage of simplicity, and are adequate for analyzing
relative benefit levels under present law and many alternative plans, both
across earnings levels and over time. However, these illustrations are not
fully satisfactory for making comparisons of benefits under individual
account plans, or other plans where benefits are dependent on the timing
as well as the amount of earnings.

Over-representing early earnings tends to bias downward
estimates of the internal rate of return of the present-law program, while
at the same time biasing upward estimates of benefit levels under plans
with individual accounts. To avoid these biases, the Office of the Chief
Actuary has developed "scaled worker" hypothetical earnings
histories. These earnings histories reflect the more typical patterns of
work and earnings levels of actual workers over their careers.

This appendix describes how the scaled worker factors
used in determining the hypothetical scaled earnings histories have been
developed. For a given age the fundamental unit, which we call
"normalized earnings", is the ratio of a worker's annual
earnings at that age to the same year's AWI. Normalized earnings for a
given age can be combined and averaged over time.

Three sets of scaled worker factors have been developed,
representing low, medium, and high lifetime earnings. (Maximum workers are
assumed to work steadily at the OASDI taxable maximum, as before.)
Initially, one set of raw scaled factors is
developed using earnings from
the Continuous Work History Sample (CWHS). Then, the
raw scaled factors
are adjusted so as to produce the same Average Indexed Monthly Earnings
(AIME)13 values as those
calculated for low, average, and high earning steady workers. This
approach has been selected in order to provide continuity with previous
estimates for steady workers. Because these adjusted lifetime earnings
levels are not designed to represent any particular points in the
distribution(s) for actual workers, familiarity with where these
hypothetical earnings histories fall in the actual distribution is
important. This is discussed in the section entitled "Discussion of
Worker Earnings and Benefit Levels" on page 7 of this note.

Developing Raw Scaled Factors
from Earnings in the CWHS

Development of the raw scaled
factors occurs in three steps:

(1) Determine which workers in the CWHS to include in the note,
(2) Tabulate the earnings for these workers, and
(3) Develop the raw scaled factors from the
tabulated earnings.

Determine Which Workers in the CWHS to Include in the Note

The CWHS is a 1-percent sample of workers who have paid
FICA taxes sometime during their lifetime. It is updated annually by the
Office of Research, Evaluation, and Statistics. The factors in this
actuarial note are developed using the 1998 version of the CWHS.

Because the CWHS contains earnings for all persons who
have paid FICA taxes sometime during their lifetime, it is important to
limit analysis only to workers who are likely to be eligible for
retirement or disability benefits, or have dependents eligible for
survivors benefits. To include only those workers, we used the status of
presently fully insured . Basically, a worker
is considered presently fully insured if he or
she has a total number of
quarters of coverage (QCs)14
at least equal to the number of years after attainment of age 21 through
the last year considered in the analysis (in this case 1997). A further
requirement is that the worker has a minimum of 6 QCs. Since permanent fully insured status is achieved with 40 QCs,
any worker with 40 QCs is
presently fully insured no matter how many years
have elapsed since age
21. Any worker who is classified as presently fully
insured is likely to
become eligible for a Social Security retirement benefit if he or she
survives to eligibility age.

Tabulate Earnings

The 1998 CWHS file contains FICA earnings for years 1951
through 1998. Due to posting delays, the earnings for 1998 in this file
are less complete than for earlier years and were not used in our
analysis. For each of the workers classified as
presently fully insured,
earnings are included of those years 1988 through 1997 for which the
worker is age 21 or over. Each year of earnings is classified by age of
worker, and is expressed as the ratio of the earnings to the AWI for the
year.

Scaled factors were developed to take into account both
the variations in earnings by age and the probabilities that workers may
have years with zero earnings. Years with zero earnings are included among
the earnings records selected. However, years in which the worker was
deceased15 or receiving
a primary Social Security benefit, are not included.

Develop Raw Scaled Factors

To normalize earnings from different years, annual
earnings amounts for each year are divided by the AWI for that year. For
each presently fully insured worker,
normalized earnings are tabulated by
age for each age 21 and over for years 1988-97, as described in the
preceding paragraph. The normalized earnings are summed by age and a
corresponding worker count is kept. The raw scaled
factors are determined
by dividing the tabulated sum for each age by the corresponding worker
count. The tabulated amounts, corresponding worker counts, and computed
raw scaled factors are shown in table A1.

Table A1.--Aggregate Normalized Earnings
(Ratio of Annual Earnings to Current AWI),
Count of Presently Fully Insured
Workers in Sample,
and Raw Scaled Factors by Age

Age

Aggregate ofnormalized earnings
(1)

Number ofearners atage
(2)

Raw scaledfactor
(1)/(2)(3)

21

105,404

342,946

0.307

22

128,562

352,727

.364

23

161,731

362,655

.446

24

193,283

373,277

.518

25

220,435

383,352

.575

26

245,216

393,115

.624

27

266,792

399,642

.668

28

284,844

404,616

.704

29

299,951

409,471

.733

30

314,626

415,055

.758

31

328,142

420,734

.780

32

339,568

424,949

.799

33

348,564

426,454

.817

34

354,484

425,037

.834

35

358,540

421,955

.850

36

359,675

417,244

.862

37

359,765

410,579

.876

38

357,027

401,947

.888

39

354,024

393,953

.899

40

351,362

386,016

.910

41

350,100

379,024

.924

42

343,972

368,139

.934

43

332,605

353,013

.942

44

320,899

338,459

.948

45

311,183

326,300

.954

46

300,599

313,654

.958

47

287,368

299,228

.960

48

273,994

285,300

.960

49

258,234

270,691

.954

50

242,447

255,910

.947

51

223,384

238,498

.937

52

208,734

225,677

.925

53

197,737

217,407

.910

54

186,183

208,673

.892

55

172,557

198,292

.870

56

158,222

188,626

.839

57

147,643

182,183

.810

58

138,212

176,889

.781

59

129,020

171,878

.751

60

119,072

167,233

.712

61

108,495

163,414

.664

62

78,296

92,170

.849

63

59,908

70,074

.855

64

49,498

59,841

.827

Adjust Raw Scaled Factors
to Match Steady Worker AIME Values

Adjustment of the raw scaled factors
occurs in four steps:

(1) Calculate preliminary adjusted scaled
factors from the raw scaled factors
(2) Construct the earnings record and calculate the AIME for a
hypothetical scaled worker using the preliminary
adjusted scaled factors
(3) Determine AIME values for low, average, and high steady workers;
and
(4) Calculate low, medium, and high scaled
factors from the preliminary adjusted scaled
factors that would give hypothetical scaled workers the same AIME
values as hypothetical steady workers.

The following values, based on table A1, show that there is
an accelerating decline in raw factors at ages 59 through 61, followed by
increases at ages 62 and 63:

Age

Raw factor

Difference

55

0.870

56

.839

-0.031

57

.810

-.029

58

.781

-.029

59

.751

-.030

60

.712

-.039

61

.664

-.048

62

.849

+.185

63

.855

+.006

64

.827

-.028

Definitive information is not available at this time on
reasons for these changes after age 59. However, it seems reasonable to
assume that some of the decline in the raw factors at ages 59 through 61
is due to retirement (total or partial) of some workers before they became
entitled to their OASDI retirement benefits at age 62. The increases in
the raw factors at ages 62 and 63 may reasonably be attributed to the fact
that healthier, higher-wage workers, and workers who have maintained
consistent employment at higher ages, are more likely to delay entitlement
to OASDI benefits until after age 62. The earnings of many non-workers,
low-wage workers, or less-healthy workers have been removed from the
tabulated group starting at age 62 because they have started to receive
retirement benefits under Social Security.

Due to the differences between the groups of workers
represented in data for just-before versus just-after age 62, a smoother
set of "adjusted" raw factors was developed for ages 62-64. The
factors were developed assuming that wages for workers over age 61 would
stay constant in nominal dollars, thus decreasing in real (constant)
dollars. The preliminary adjusted scaled factors
are set equal to the raw
scaled factors for ages through 61. Factors for ages 62 and over are
calculated so that earnings in nominal dollars stay constant at the level
for age 61. For example, the preliminary adjusted factor for age 62 is
calculated by dividing the factor for age 61 by the ultimate assumed
annual increase in average wages under the intermediate assumptions of the
2001 Trustees Report. The calculation of the preliminary
adjusted scaled factors for ages 62-64 is shown in table A2.

This approach, while providing an imperfect approximation
for all types of workers, was adopted in order to avoid having different
scales for workers who become entitled to OASDI benefits at different
ages.

Table A2.--Scaled Factor Adjustments Made for Ages After 61

Age

61

62

63

64

Raw scaled factor

0.664

0.849

0.855

0.827

Ultimate AWI increase since age 61,
based on 2001 Trustees Report, Intermediate Assumptions

Construct the Earnings Record and Calculate the
AIME for a Hypothetical Scaled Worker Using the Preliminary Adjusted
Scaled Factors

This hypothetical scaled worker is assumed to have date
of birth January 2, 1950, to have earnings from age 21 through age 64, and
to retire at age 65. Earnings for each year are calculated by multiplying
the preliminary adjusted scaled factor for that
age by the AWI value for the corresponding year. This hypothetical scaled worker based on the
preliminary adjusted scaled factors turns age 22 in 1972. So the age 22
factor of 0.364 is multiplied by the 1972 AWI of $7,133.80 to obtain
annual earnings of $2,596.70. Table A3 shows the
preliminary adjusted scaled factors,
AWI amounts, and corresponding hypothetical earnings for this
hypothetical worker. The earnings record thus constructed has an AIME value
of $3,526 for this worker.

Table A3.--Computation of the Earnings Record and the AIME for theTheoretical
Scaled Worker Born in 1950 Based on thePreliminary Adjusted Scaled Factors
and the AWI Series

Year

Age

Preliminaryadjustedscaled factors
(1)

AWI forcurrent year
(2)

Estimatedearnings forcurrent year
(1)*(2)(3)

1971

21

0.307

$6,497.08

$1,994.60

1972

22

.364

7,133.80

2,596.70

1973

23

.446

7,580.16

3,380.75

1974

24

.518

8,030.76

4,159.93

1975

25

.575

8,630.92

4,962.78

1976

26

.624

9,226.48

5,757.32

1977

27

.668

9,779.44

6,532.67

1978

28

.704

10,556.03

7,431.45

1979

29

.733

11,479.46

8,414.44

1980

30

.758

12,513.46

9,485.20

1981

31

.780

13,773.10

10,743.02

1982

32

.799

14,531.34

11,610.54

1983

33

.817

15,239.24

12,450.46

1984

34

.834

16,135.07

13,456.65

1985

35

.850

16,822.51

14,299.13

1986

36

.862

17,321.82

14,931.41

1987

37

.876

18,426.51

16,141.62

1988

38

.888

19,334.04

17,168.63

1989

39

.899

20,099.55

18,069.50

1990

40

.910

21,027.98

19,135.46

1991

41

.924

21,811.60

20,153.92

1992

42

.934

22,935.42

21,421.68

1993

43

.942

23,132.67

21,790.98

1994

44

.948

23,753.53

22,518.35

1995

45

.954

24,705.66

23,569.20

1996

46

.958

25,913.90

24,825.52

1997

47

.960

27,426.00

26,328.96

1998

48

.960

28,861.44

27,706.98

1999

49

.954

30,469.84

29,068.23

2000

50

.947

32,104.67

30,403.12

2001

51

.937

33,680.35

31,558.49

2002

52

.925

35,277.03

32,631.25

2003

53

.910

36,781.09

33,470.79

2004

54

.892

38,372.33

34,228.12

2005

55

.870

40,044.65

34,838.85

2006

56

.839

41,799.45

35,069.74

2007

57

.810

43,575.71

35,296.33

2008

58

.781

45,416.27

35,470.11

2009

59

.751

47,350.68

35,560.36

2010

60

.712

49,366.08

35,148.65

2011

61

.664

51,488.82

34,188.58

2012

62

.637

53,702.84

34,188.58

2013

63

.610

56,012.06

34,188.58

2014

64

.585

58,420.58

34,188.58

AIME

3,526

Determine AIME Values for Low, Average, and High Steady Workers

AIME values are determined for three different steady
workers, denoted as low, average, and high steady workers. All three
steady workers are assumed to be born on January 2, 1950, to retire
February 1, 2015, and to have steady earnings from age 22 (1972) through
age 64 (2014). The only difference among the three is the level of
earnings. For the low steady worker, each year of earnings is assumed to
equal 45 percent of the AWI. For the average steady worker, each year of
earnings is assumed to equal the AWI. For the high steady worker, each
year of earnings is assumed to equal 160 percent of AWI. For years in
which actual historical AWI values are not available, we use the AWI
levels assumed for the intermediate assumptions of the 2001 Trustees
Report. The earnings records, along with calculated AIMEs, for our three
steady workers are given in table A4, as follows:

Table A4.--Three Hypothetical Steady Workers
Born in 1950: Their Earnings and Their AIMEs

Year

Age

AWI

Low Worker45% of AWI

Average Worker100% of AWI

High Worker160% of AWI

1971

21

$6,497.08

$2,923.69

$6,497.08

$7,800.00

1972

22

7,133.80

3,210.21

7,133.80

9,000.00

1973

23

7,580.16

3,411.07

7,580.16

10,800.00

1974

24

8,030.76

3,613.84

8,030.76

12,849.22

1975

25

8,630.92

3,883.91

8,630.92

13,809.47

1976

26

9,226.48

4,151.92

9,226.48

14,762.37

1977

27

9,779.44

4,400.75

9,779.44

15,647.10

1978

28

10,556.03

4,750.21

10,556.03

16,889.65

1979

29

11,479.46

5,165.76

11,479.46

18,367.14

1980

30

12,513.46

5,631.06

12,513.46

20,021.54

1981

31

13,773.10

6,197.90

13,773.10

22,036.96

1982

32

14,531.34

6,539.10

14,531.34

23,250.14

1983

33

15,239.24

6,857.66

15,239.24

24,382.78

1984

34

16,135.07

7,260.78

16,135.07

25,816.11

1985

35

16,822.51

7,570.13

16,822.51

26,916.02

1986

36

17,321.82

7,794.82

17,321.82

27,714.91

1987

37

18,426.51

8,291.93

18,426.51

29,482.42

1988

38

19,334.04

8,700.32

19,334.04

30,934.46

1989

39

20,099.55

9,044.80

20,099.55

32,159.28

1990

40

21,027.98

9,462.59

21,027.98

33,644.77

1991

41

21,811.60

9,815.22

21,811.60

34,898.56

1992

42

22,935.42

10,320.94

22,935.42

36,696.67

1993

43

23,132.67

10,409.70

23,132.67

37,012.27

1994

44

23,753.53

10,689.09

23,753.53

38,005.65

1995

45

24,705.66

11,117.55

24,705.66

39,529.06

1996

46

25,913.90

11,661.26

25,913.90

41,462.24

1997

47

27,426.00

12,341.70

27,426.00

43,881.60

1998

48

28,861.44

12,987.65

28,861.44

46,178.30

1999

49

30,469.84

13,711.43

30,469.84

48,751.74

2000

50

32,104.67

14,447.10

32,104.67

51,367.47

2001

51

33,680.35

15,156.16

33,680.35

53,888.56

2002

52

35,277.03

15,874.66

35,277.03

56,443.25

2003

53

36,781.09

16,551.49

36,781.09

58,849.74

2004

54

38,372.33

17,267.55

38,372.33

61,395.73

2005

55

40,044.65

18,020.09

40,044.65

64,071.44

2006

56

41,799.45

18,809.75

41,799.45

66,879.12

2007

57

43,575.71

19,609.07

43,575.71

69,721.14

2008

58

45,416.27

20,437.32

45,416.27

72,666.03

2009

59

47,350.68

21,307.81

47,350.68

75,761.09

2010

60

49,366.08

22,214.74

49,366.08

78,985.73

2011

61

51,488.82

23,169.97

51,488.82

82,382.11

2012

62

53,702.84

24,166.28

53,702.84

85,924.54

2013

63

56,012.06

25,205.43

56,012.06

89,619.30

2014

64

58,420.58

26,289.26

58,420.58

93,472.93

AIME

1,874

4,166

6,666

Calculate Low, Medium, and High Scaled Factors from
the Preliminary Adjusted Scaled Factors

To maintain continuity with each of the three steady
worker estimates, the preliminary adjusted scaled
factors are further
adjusted so that the AIME value for the scaled worker matches the AIME
value for the corresponding steady worker. This requires three separate
calculations, one each for the low, medium, and high earnings cases. For
example, the scaled factors for the hypothetical medium scaled worker are
determined by multiplying:

(1) The preliminary adjusted scaled factors
for ages 22 through 64,
by;
(2) The ratio of the average steady worker AIME to the scaled worker
AIME.

Repeating the above procedure with low and high steady
worker AIME values, we obtain the final scaled factors
for the low and
high workers. Table A5 gives the details of the calculation of the three AIME
ratios.

Table A6 shows the calculation of the final
scaled factors, combining the
preliminary adjusted scaled factors and the AIME
ratios.

Table A6.--Calculation of Final Scaled Factors

Adjustment factors ----------------->

Earnings level

Low

Medium

High

0.532

1.182

1.891

Age

Preliminary adjustedscaled factors

Final scaled factors

21

0.307

0.163

0.363

0.581

22

.364

.193

.430

.688

23

.446

.237

.527

.843

24

.518

.275

.612

.979

25

.575

.306

.679

1.087

26

.624

.332

.737

1.180

27

.668

.355

.789

1.263

28

.704

.374

.832

1.331

29

.733

.390

.866

1.386

30

.758

.403

.896

1.433

31

.780

.415

.922

1.475

32

.799

.425

.944

1.511

33

.817

.434

.965

1.545

34

.834

.443

.985

1.577

35

.850

.452

1.004

1.607

36

.862

.458

1.018

1.630

37

.876

.466

1.035

1.656

38

.888

.472

1.049

1.679

39

.899

.478

1.062

1.700

40

.910

.484

1.075

1.720

41

.924

.491

1.092

1.747

42

.934

.496

1.104

1.766

43

.942

.501

1.113

1.781

44

.948

.504

1.120

1.792

45

.954

.507

1.127

1.804

46

.958

.509

1.132

1.811

47

.960

.510

1.134

1.815

48

.960

.510

1.134

1.815

49

.954

.507

1.127

1.804

50

.947

.503

1.119

1.790

51

.937

.498

1.107

1.771

52

.925

.492

1.093

1.749

53

.910

.484

1.075

1.720

54

.892

.474

1.054

1.686

55

.870

.462

1.028

1.645

56

.839

.446

.991

1.586

57

.810

.430

.957

1.531

58

.781

.415

.923

1.477

59

.751

.399

.887

1.420

60

.712

.378

.841

1.346

61

.664

.353

.785

1.255

62

.637

.339

.753

1.204

63

.610

.324

.721

1.153

64

.585

.311

.691

1.106

Developing Hypothetical Worker Earnings from Factors

Given a year of birth, and an earnings level for scaled
workers, classified as either low, medium, or high workers, annual
earnings can be obtained by taking the relevant set of
scaled factors and
multiplying them by the AWIs in the corresponding years. Consider as an
example a low earnings worker born in 1970. To determine earnings for this
worker at age 22, the scaled factor for the low
worker at age 22 would be
multiplied by the AWI in 1992, the year in which the worker turns 22.
Because the hypothetical workers are born in January, a year of age
corresponds to a calendar year. Therefore, a worker born on January 2,
1970 would be age 22 throughout 1992. Earnings for other ages are
determined in the same manner. In this manner, a series of low, medium,
and high scaled earnings can be developed for any hypothetical year of
birth. Table A7 carries out the calculation of hypothetical scaled worker
earnings for the high earnings workers for the selected years of birth
1930, 1949, and 1997.

Table A7.--Calculation of Scaled Earnings for High Earnings Workers for
Years of Birth 1930, 1949, and 1997

Year of birth--------->

1930

1949

1997

Age

Final scaledfactors forhigh earner(1)

AWI(2)

Age-scaledearnings
(1)*(2)(3)

AWI
(4)

Age-scaledearnings
(1)*(4)(5)

AWI
(6)

Age-scaledearnings
(1)*(6)(7)

22

0.688

$2,973.32

$2,046.10

$6,497.08

$4,470.98

$72,108.66

$49,621.72

23

.843

3,139.44

2,647.10

7,133.80

6,015.04

75,209.33

63,414.65

24

.979

3,155.64

3,090.30

7,580.16

7,423.20

78,443.33

76,819.02

25

1.087

3,301.44

3,588.84

8,030.76

8,729.86

81,816.39

88,938.78

26

1.180

3,532.36

4,167.09

8,630.92

10,181.80

85,334.50

100,668.19

27

1.263

3,641.72

4,599.03

9,226.48

11,651.87

89,003.88

112,400.54

28

1.331

3,673.80

4,889.58

9,779.44

13,015.76

92,831.05

123,551.76

29

1.386

3,855.80

5,343.20

10,556.03

14,628.09

96,822.78

134,172.81

30

1.433

4,007.12

5,742.28

11,479.46

16,450.29

100,986.16

144,715.17

31

1.475

4,086.76

6,026.38

12,513.46

18,452.49

105,328.57

155,318.72

32

1.511

4,291.40

6,482.29

13,773.10

20,804.70

109,857.70

165,943.51

33

1.545

4,396.64

6,790.88

14,531.34

22,444.54

114,581.58

176,978.24

34

1.577

4,576.32

7,215.48

15,239.24

24,027.71

119,508.59

188,429.19

35

1.607

4,658.72

7,486.32

16,135.07

25,928.22

124,647.45

200,302.02

36

1.630

4,938.36

8,047.72

16,822.51

27,414.55

130,007.30

211,864.41

37

1.656

5,213.44

8,633.99

17,321.82

28,686.70

135,597.61

224,563.49

38

1.679

5,571.76

9,353.81

18,426.51

30,934.21

141,428.31

237,428.21

39

1.700

5,893.76

10,016.94

19,334.04

32,859.83

147,509.72

250,705.19

40

1.720

6,186.24

10,642.68

20,099.55

34,578.86

153,852.64

264,685.01

41

1.747

6,497.08

11,349.41

21,027.98

36,732.67

160,468.30

280,313.64

42

1.766

7,133.80

12,596.53

21,811.60

38,513.89

167,368.44

295,531.27

43

1.781

7,580.16

13,499.33

22,935.42

40,845.16

174,565.28

310,879.28

44

1.792

8,030.76

14,392.89

23,132.67

41,458.84

182,071.59

326,312.36

45

1.804

8,630.92

15,566.41

23,753.53

42,840.99

189,900.67

342,497.87

46

1.811

9,226.48

16,710.31

24,705.66

44,745.05

198,066.40

358,723.08

47

1.815

9,779.44

17,748.77

25,913.90

47,031.30

206,583.25

374,929.26

48

1.815

10,556.03

19,158.21

27,426.00

49,775.62

215,466.33

391,051.22

49

1.804

11,479.46

20,703.93

28,861.44

52,053.43

224,731.39

405,317.27

50

1.790

12,513.46

22,403.22

30,469.84

54,551.05

234,394.84

419,644.01

51

1.771

13,773.10

24,398.00

32,104.67

56,870.99

244,473.81

433,066.84

52

1.749

14,531.34

25,411.51

33,680.35

58,898.11

254,986.19

445,904.03

53

1.720

15,239.24

26,217.28

35,277.03

60,689.90

265,950.59

457,536.09

54

1.686

16,135.07

27,209.38

36,781.09

62,025.81

277,386.47

467,770.82

55

1.645

16,822.51

27,668.97

38,372.33

63,113.23

289,314.09

475,851.93

56

1.586

17,321.82

27,475.05

40,044.65

63,516.92

301,754.59

478,628.82

57

1.531

18,426.51

28,217.02

41,799.45

64,008.64

314,730.04

481,954.70

58

1.477

19,334.04

28,546.75

43,575.71

64,339.62

328,263.43

484,681.61

59

1.420

20,099.55

28,537.06

45,416.27

64,481.39

342,378.76

486,104.62

60

1.346

21,027.98

28,304.83

47,350.68

63,736.65

357,101.05

480,677.86

61

1.255

21,811.60

27,380.33

49,366.08

61,969.75

372,456.39

467,548.33

62

1.204

22,935.42

27,620.35

51,488.82

62,006.24

388,472.02

467,823.65

63

1.153

23,132.67

26,677.10

53,702.84

61,931.28

405,176.31

467,258.15

64

1.106

23,753.53

26,270.42

56,012.06

61,947.02

422,598.90

467,376.88

1
Because the OASDI trust funds receive transfers
from the General Fund of the Treasury equal to a portion of taxes on
benefits, internal rates of return that ignore these transfers may
arguably overstate the return on contributions. Due to the difficulty of
determining the level of income tax on benefits, this relatively small
factor is not addressed in this note.

2
"Average wage" refers to the Social
Security average wage index for the entire economy. The Social Security
average wage index is based on the average amount of total wages for each
year after 1950, including wages in both covered and noncovered employment
and wages in excess of the OASDI contribution and benefit base. A table of
the historical average wage index is available at
www.socialsecurity.gov/OACT/COLA/AWI.html. The 2001 Trustees Report
projections of future average wage amounts are available at
www.socialsecurity.gov/OACT/TR/TR01/lr6E7-2.html.

3
For certain historical years, earnings of 160
percent of the average wage would exceed the OASDI Contribution and
Benefit Base; amounts above such Contribution and Benefit Base are not
included in the computation of internal rate of return.

4
The OASDI Contribution and Benefit Base, also known
as the "wage base" and as the "taxable maximum", is
the annual dollar amount above which earnings in employment covered under
the OASDI program are neither taxable nor creditable for benefit
computation purposes. Further information about the OASDI Contribution and
Benefit Base can be found at www.socialsecurity.gov/OACT/COLA/cbb.html.

5
In this context, an actual
worker is said to be "best represented" by a particular
hypothetical worker if that hypothetical worker's PIA is closest to the
actual worker's PIA. As an illustration, table 1
shows that 44.0 percent of actual retirees have a PIA
that is closer to the PIA of the low-earning worker than to any other, and
are thus said to be best represented by the low-earning worker.

6
Average Indexed Monthly Earnings. The AIME value
represents the beneficiary's average monthly earnings after indexing for
wage growth in the economy in his or her highest years of earnings. The
procedure for calculating the AIME is illustrated at
www.socialsecurity.gov/OACT/. Select "Compute Your Own Benefit".

7
An exposition of the procedures for calculating the
salary scale factors is presented in the appendix of this note. The salary
scale factor values are presented in table A6.

8
For the "in-between years" of the
series of tables 3, 4, 5, and 6, the factors affecting the internal rate
of return, and their qualitative effects, are known (all factors of one
year in relation to a comparison year): mortality improvements increase
the internal rate of return; benefit increases (decreases--including an
increase in the NRA) increase (decrease) the internal rate of return; and
tax increases decrease the internal rate of return. However, an
explanation of the intermediate ups and downs of each series would require
quantitative measures of the different effects of each factor. The
development and analysis of such measures is beyond the scope of this
note.

9
For comparability in these calculations, the
benefits of workers retiring at ages other than 62 were adjusted by wage
indexing to make them equivalent to those of age 62 retirees.

12
For example if she is single with a medium
earnings record, her internal rate of return is about 25 percent more than
her male counterpart.

13
The AIME value represents the beneficiary's
average monthly earnings, after indexing for wage growth in the economy,
in his or her highest years of earnings.

14
The QC is the basic unit for determining whether
a worker is insured for Social Security benefits. In 1997, for example, a
worker needed to have $670 in covered earnings to obtain a QC. Workers can
earn up to 4 QC's per calendar year. Since 1978 the amount of covered
earnings required to obtain a QC has been automatically indexed each year
with the growth in the SSA official average wage index. See
www.socialsecurity.gov/OACT/COLA/QC.html for more information, including a
list of historical QC amounts.

15
Data concerning worker deaths was taken from the
CWHS. Death data in the CWHS may be somewhat understated.